Problem: Solve for $x$ and $y$ using elimination. ${-5x+y = -6}$ ${-3x-4y = -45}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ ${-20x+4y = -24}$ $-3x-4y = -45$ Add the top and bottom equations together. $-23x = -69$ $\dfrac{-23x}{{-23}} = \dfrac{-69}{{-23}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-5x+y = -6}\thinspace$ to find $y$ ${-5}{(3)}{ + y = -6}$ $-15+y = -6$ $-15{+15} + y = -6{+15}$ ${y = 9}$ You can also plug ${x = 3}$ into $\thinspace {-3x-4y = -45}\thinspace$ and get the same answer for $y$ : ${-3}{(3)}{ - 4y = -45}$ ${y = 9}$